Theory of Anode Region of Short High-Current Vacuum Arc

A model of the anode region of a high-current vacuum arc is developed, which explicitly takes into consideration the ratio of the drift velocity of the electrons in plasma $v_{0}$ to their thermal velocity $v_{T}$ as a parameter of the electron velocity distribution function in the anode sheath. A transcendental equation for determining the value of the negative anode drop (AD) as a function of ratio $v_{0}/v_{T}$ is obtained. It is shown that, in contrast to the well-known Langmuir formula in a 1-D model of a collisionless sheath, the AD remains negative for any value of $v_{0}/v_{T}$ relation. For small values of $v_{0}/v_{T} \ll 1$ , the expression obtained asymptotically passes into the Langmuir formula. The dependence of the AD value on the current density is used as a boundary condition at the anode in solving the 2-D problems in the theory of short vacuum arc. In accordance with the Langmuir formula, a region with a positive AD is formed at the anode when the current density increases. The results of this paper show that the region with a positive AD is absent.